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# Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x).

Since f is a linear function, f (x) = mx + c. Also, since (1, 1), (0, – 1) $\in$ R, f (1) = m + c = 1 and f (0) = c = –1. This gives m = 2 and f(x) = 2x – 1.